300 r
10 15 20 25 30 35 40 45 50
Figure 2. Income per worker at 0, 2, and 3 percent population growth over 50 years.
percent per year. The income per worker is approximately 16 percent higher for the rapidly growing population at the end of 25 years. If we assume a three to one ratio in income of those entering as against those leaving (case IV), the per worker income is 25 percent higher at the end of 25 years. However, at the end of 50 years, when full replacement takes place under all assumptions, the per capita income is the same for all rates of population growth. This, however, omits the likelihood that during this 50-year period further increases take place in the education of those who enter compared to earlier entrants and hence the replacement effect continues to operate until the point is reached where the productivity of those who enter ceases to be higher than the productivity of those who leave.* Also, the illustration omits the effects of higher savings and investment out of the higher income per worker on income growth.
Of course the results depend on the assumption. But we can weaken some of our assumptions without altering the general point made. For example, assume that beyond some point there are diminishing returns to education at
*A model in which there was a gradual shift from 10 percent of the entrants receiving 6 years of education to 100 percent over a period of 10 years gave approximately similar results for the twentieth year. In other words, the 3 percent growth population earned more than 25 percent more income per worker than the stationary population in year onn is greater on the average than those with less.*